For a given input value $q$, the function $f$ outputs a value $r$ to satisfy the following equation. $11q-4=3r-6$ Write a formula for $f(q)$ in terms of $q$. $f(q)=$
Answer: $f(q)$ expresses $r$ as a function of $q$. To arrive at a correct formula, all we have to do is solve the equation for $r$. $ \begin{aligned}11q-4&=3r-6\\\\ 11q+2&=3r\\\\ \dfrac{11q}{3}+\dfrac{2}{3}&=r\end{aligned}$ Therefore, this formula expresses $r$ as a function of $q$ : $ f(q)=\dfrac{11}{3}q+\dfrac{2}{3}$